Dual Nature Of Light Question 348
Question: A proton has kinetic energy E = 100 keV which is equal to that of a photon. The wavelength of photon is $ {\lambda_{2}} $ and that of proton is $ {\lambda_{1}}. $ The ration of $ {\lambda_{2}}/{\lambda_{1}} $ is proportional to
Options:
A) $ E^{2} $
B) $ {{E}^{1/2}} $
C) $ {{E}^{-1}} $
D) $ {{E}^{-1/2}} $
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Answer:
Correct Answer: D
Solution:
[d] For photon, $ {\lambda_{2}}=\frac{hc}{E} $ ?.(i) For proton, $ p=\sqrt{2mE} $ $ {\lambda_{1}}=\frac{h}{p}=\frac{h}{\sqrt{2mE}} $ ?(ii) $ \frac{{\lambda_{2}}}{{\lambda_{1}}}=\frac{hc}{E\times \frac{h}{\sqrt{2mE}}}\propto {{E}^{-1/2}} $
BETA
